Relevant bibliographies by topics / Diagram algebra

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Diagram algebra'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Diagram algebra"

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COHEN, ARJEH M., DIÉ A. H. GIJSBERS, and DAVID B. WALES. "TANGLE AND BRAUER DIAGRAM ALGEBRAS OF TYPE Dn." Journal of Knot Theory and Its Ramifications 18, no. 04 (April 2009): 447–83. http://dx.doi.org/10.1142/s0218216509007063.

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A generalization of the Kauffman tangle algebra is given for Coxeter type D n. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman–Murakami–Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is A n - 1. The proof involves a diagrammatic version of the Brauer algebra of type D n of which the generalized Temperley–Lieb algebra of type D n is a subalgebra.
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DUCHAMP, G. H. E., J. G. LUQUE, J. C. NOVELLI, C. TOLLU, and F. TOUMAZET. "HOPF ALGEBRAS OF DIAGRAMS." International Journal of Algebra and Computation 21, no. 06 (September 2011): 889–911. http://dx.doi.org/10.1142/s0218196711006418.

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We investigate several generalizations of the Hopf algebra MQSym whose constructions come from labelings of special diagrams in bijection with packed matrices. Their products come either from the Hopf algebras WSym or WQSym, respectively built on integer set partitions and set compositions. Realizations on bi-word are exhibited, and it is shown how these algebras fit into a commutative diagram. Hopf deformations and dendriform structures are also considered for some algebras in the picture.
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Rezaei, Akbar, Arsham Borumand Saeid, and Andrzej Walendziak. "Some results on pseudo-Q algebras." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (December 1, 2017): 61–72. http://dx.doi.org/10.1515/aupcsm-2017-0005.

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AbstractThe notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.
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Matsumoto, Kengo. "C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems." Journal of the Australian Mathematical Society 81, no. 3 (December 2006): 369–85. http://dx.doi.org/10.1017/s1446788700014373.

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AbstractA λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. InDoc. Math.7 (2002) 1–30, the author constructed aC*-algebraO£associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebraO£, under a certain condition on £ called (II). As a result, the class of theC*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.
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Fuller, Kent R., and Koichiro Ohtake. "Strong module diagrams and frobenius diagram algebras." Communications in Algebra 17, no. 2 (January 1989): 259–98. http://dx.doi.org/10.1080/00927878908823727.

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GREEN, R. M. "GENERALIZED TEMPERLEY–LIEB ALGEBRAS AND DECORATED TANGLES." Journal of Knot Theory and Its Ramifications 07, no. 02 (March 1998): 155–71. http://dx.doi.org/10.1142/s0218216598000103.

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We give presentations, by means of diagrammatic generators and relations, of the analogues of the Temperley–Lieb algebras associated as Hecke algebra quotients to Coxeter graphs of type B and D. This generalizes Kauffman's diagram calculus for the Temperley–Lieb algebra.
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Laudone, Robert P. "The spin-Brauer diagram algebra." Journal of Algebraic Combinatorics 50, no. 2 (October 15, 2018): 191–224. http://dx.doi.org/10.1007/s10801-018-0849-8.

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GRABOWSKI, JAN E. "ON LIE INDUCTION AND THE EXCEPTIONAL SERIES." Journal of Algebra and Its Applications 04, no. 06 (December 2005): 707–37. http://dx.doi.org/10.1142/s0219498805001496.

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Lie bialgebras occur as the principal objects in the infinitesimalization of the theory of quantum groups — the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to classical questions. In this paper, we study the simple complex Lie algebras using the double-bosonization construction of Majid. This construction expresses algebraically the induction process given by adding and removing nodes in Dynkin diagrams, which we call Lie induction. We first analyze the deletion of nodes, corresponding to the restriction of adjoint representations to subalgebras. This uses a natural grading associated to each node. We give explicit calculations of the module and algebra structures in the case of the deletion of a single node from the Dynkin diagram for a simple Lie (bi-)algebra. We next consider the inverse process, namely that of adding nodes, and give some necessary conditions for the simplicity of the induced algebra. Finally, we apply these to the exceptional series of simple Lie algebras, in the context of finding obstructions to the existence of finite-dimensional simple complex algebras of types E9, F5 and G3. In particular, our methods give a new point of view on why there cannot exist such an algebra of type E9.
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Tyler, Jason. "Every AF-algebra is Morita equivalent to a graph algebra." Bulletin of the Australian Mathematical Society 69, no. 2 (April 2004): 237–40. http://dx.doi.org/10.1017/s0004972700035978.

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Denecke, K., J. Koppitz, and R. Marszałek. "Derived Varieties and Derived Equational Theories." International Journal of Algebra and Computation 08, no. 02 (April 1998): 153–69. http://dx.doi.org/10.1142/s0218196798000090.

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This paper describes a derivation process for varieties and equational theories using the theory of hypersubstitutions and M-hyperidentities. A hypersubstitution σ of type τ is a map which takes each n-ary operation symbol of the type to an n-ary term of this type. If [Formula: see text] is an algebra of type τ then the algebra [Formula: see text] is called a derived algebra of [Formula: see text]. If V is a class of algebras of type τ then one can consider the variety vσ(V) generated by the class of all derived algebras from V. In the first two sections the necessary definitions are given. In Sec. 3 the properties of derived varieties and derived equational theories are described. On the set of all derived varieties of a given variety, a quasiorder is developed which gives a derivation diagram. In the final section the derivation diagram for the largest solid variety of medial semigroups is worked out.
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Dissertations / Theses on the topic "Diagram algebra"

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Ahmed, Chwas Abas. "Representation theory of diagram algebras : subalgebras and generalisations of the partition algebra." Thesis, University of Leeds, 2016. http://etheses.whiterose.ac.uk/15997/.

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This thesis concerns the representation theory of diagram algebras and related problems. In particular, we consider subalgebras and generalisations of the partition algebra. We study the d-tonal partition algebra and the planar d-tonal partition algebra. Regarding the d-tonal partition algebra, a complete description of the J -classes of the underlying monoid of this algebra is obtained. Furthermore, the structure of the poset of J -classes of the d-tonal partition monoid is also studied and numerous combinatorial results are presented. We observe a connection between canonical elements of the d-tonal partition monoids and some combinatorial objects which describe certain types of hydrocarbons, by using the alcove system of some reflection groups. We show that the planar d-tonal partition algebra is quasi-hereditary and generically semisimple. The standard modules of the planar d-tonal partition algebra are explicitly constructed, and the restriction rules for the standard modules are also given. The planar 2-tonal partition algebra is closely related to the two coloured Fuss-Catalan algebra. We use this relation to transfer information from one side to the other. For example, we obtain a presentation of the 2-tonal partition algebra by generators and relations. Furthermore, we present a necessary and sufficient condition for semisimplicity of the two colour Fuss-Catalan algebra, under certain known restrictions.
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Wilcox, Stewart. "Cellularity of Twisted Semigroup Algebras of Regular Semigroups." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/720.

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There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.
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Corwin, Stephen P. "Representation theory of the diagram An over the ring k[[x]]." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/50001.

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Fix R = k[[x]]. Let Qn be the category whose objects are ((M₁,...,Mn),(f₁,...,fn-1)) where each Mi is a free R-module and fi:Mi⟶Mi+1 for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let βn be the full subcategory of Ωn in which each map fi is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ωn⟶βn. If X is an object of βn, we say that X diagonalizes if X is isomorphic to a direct sum of objects ((M₁,...,Mn),(f₁,...,fn-1)) in which each Mi is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of βn, and which fails only in case X is not diagonalizable. Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable.
Ph. D.
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Wilcox, Stewart. "Cellularity of Twisted Semigroup Algebras of Regular Semigroups." University of Sydney. Mathematics and Statistics, 2006. http://hdl.handle.net/2123/720.

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There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.
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Aguirre, Diana. "PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/624.

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Abstract In this project, we searched for new constructions and symmetric presentations of important groups, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. My target nonabelian simple groups included sporadic groups, linear groups, and alternating groups. In addition, we discovered finite groups as homomorphic images of progenitors and proved some of their isomorphism type and original symmetric presentations. In this thesis we found original symmeric presentations of M12, J1 and the simplectic groups S(4,4) and S(3,4) on various con- trol groups. Using the technique of double coset enumeration we constucted J2 as a homomorphic image of the permutation progenitor 2∗10 : (10 × 2). From our mono- mial progenitor 11∗4 : (2 : 4) we found a homomorphic image of M11. In the following chapters we will discuss how we went about obtaining homomorphic images, some con- structions of the Cayley Diagrams, and how we solved some extension problems.
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Michael, Ifeanyi Friday. "On a unified categorical setting for homological diagram lemmas." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/18085.

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Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: Some of the diagram lemmas of Homological Algebra, classically known for abelian categories, are not characteristic of the abelian context; this naturally leads to investigations of those non-abelian categories in which these diagram lemmas may hold. In this Thesis we attempt to bring together two different directions of such investigations; in particular, we unify the five lemma from the context of homological categories due to F. Borceux and D. Bourn, and the five lemma from the context of modular semi-exact categories in the sense of M. Grandis.
AFRIKAANSE OPSOMMING: Verskeie diagram lemmata van Homologiese Algebra is aanvanklik ontwikkel in die konteks van abelse kategorieë, maar geld meer algemeen as dit behoorlik geformuleer word. Dit lei op ’n natuurlike wyse na ’n ondersoek van ander kategorieë waar hierdie lemmas ook geld. In hierdie tesis bring ons twee moontlike rigtings van ondersoek saam. Dit maak dit vir ons moontlik om die vyf-lemma in die konteks van homologiese kategoieë, deur F. Borceux en D. Bourn, en vyflemma in die konteks van semi-eksakte kategorieë, in die sin van M. Grandis, te verenig.
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Antrobus, Jared E. "The State of Lexicodes and Ferrers Diagram Rank-Metric Codes." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/66.

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In coding theory we wish to find as many codewords as possible, while simultaneously maintaining high distance between codewords to ease the detection and correction of errors. For linear codes, this translates to finding high-dimensional subspaces of a given metric space, where the induced distance between vectors stays above a specified minimum. In this work I describe the recent advances of this problem in the contexts of lexicodes and Ferrers diagram rank-metric codes. In the first chapter, we study lexicodes. For a ring R, we describe a lexicographic ordering of the left R-module Rn. With this ordering we set up a greedy algorithm which sequentially selects vectors for which all linear combinations satisfy a given property. The resulting output is called a lexicode. This process was discussed earlier in the literature for fields and chain rings. We describe a generalization of the algorithm to finite principal ideal rings. In the second chapter, we investigate Ferrers diagram rank-metric codes, which play a role in the construction of subspace codes. A well-known upper bound for dimension of these codes is conjectured to be sharp. We describe several solved cases of the conjecture, and further contribute new ones. In addition, probabilities for maximal Ferrers diagram codes and MRD codes are investigated in a new light. It is shown that for growing field size, the limiting probability depends highly on the Ferrers diagram.
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Bowman, Christopher David. "Algebraic groups, diagram algebras, and their Schur-Weyl dualities." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610216.

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Imaev, Aleksey A. "Hierarchical Modeling of Manufacturing Systems Using Max-Plus Algebra." Ohio University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1257871858.

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King, Oliver. "The representation theory of diagram algebras." Thesis, City University London, 2014. http://openaccess.city.ac.uk/5915/.

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In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of the corresponding affine reflection group, we give a characterisation of the (limiting) blocks of the Brauer and partition algebras in positive characteristic. In the case of the Brauer algebra, we then show that simple reflections give rise to non-zero decomposition numbers. We then restrict our attention to a particular family of Brauer and partition algebras, and use the block result to determine the entire decomposition matrix of the algebras therein.
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Books on the topic "Diagram algebra"

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Conference Board of the Mathematical Sciences and NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules (2011 : Raleigh, N.C.), eds. Deformation theory of algebras and their diagrams. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2012.

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Jain, S. K., ed. Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/conm/456.

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Habiro, Kazuo. Symplectic Jacobi diagrams and the Lie algebra of homology cylinders. Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University, 2007.

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Combinatorial foundation of homology and homotopy: Applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions. Berlin: Springer, 1999.

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Baues, Hans J. Combinatorial foundation of homology and homotopy: Applications to spaces, diagrams, transformation groups, compactifications, differential algebras, algebraic theories, simplicial objects, and resolutions. Berlin: Springer, 1999.

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Japan) RIMS Camp-style Seminar "Algebraic combinatorics related to Young diagram and statistical physics" (2012 August 6-10 Kizugawa-shi. Algebraic combinatorics related to Young diagram and statistical physics: August 6-10, 2012. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2014.

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1956-, Lapidus Michel L., ed. Generalized Dyson series, generalized Feynman diagrams, the Feynman integral, and Feynman's operational calculus. Providence, R.I., USA: American Mathematical Society, 1986.

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Lipman, Joseph. Foundations of Grothendieck duality for diagrams of schemes. Berlin: Springer, 2009.

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1962-, Hashimoto Mitsuyasu, ed. Foundations of Grothendieck duality for diagrams of schemes. Berlin: Springer, 2009.

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J, Monkhorst Hendrik, and Freeman David L, eds. Algebraic and diagrammatic methods in many-fermion theory. New York: Oxford University Press, 1992.

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Book chapters on the topic "Diagram algebra"

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Shalile, Armin. "On Decomposition Numbers of Diagram Algebras." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 587–609. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_26.

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Adamou, I., M. Fioravanti, L. Gonzalez-Vega, and B. Mourrain. "Bisectors and Voronoï Diagram of a Family of Parallel Half-Lines." In SAGA – Advances in ShApes, Geometry, and Algebra, 241–79. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08635-4_13.

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Rolfsen, Dale. "The Quest for a Knot with Trivial Jones Polynomial: Diagram Surgery and the Temperley-Lieb Algebra." In Topics in Knot Theory, 195–210. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1695-4_10.

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Monk, J. Donald. "Diagrams." In Cardinal Invariants on Boolean Algebras, 248–70. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0346-0334-8_26.

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Monk, J. Donald. "Diagrams." In Cardinal Invariants on Boolean Algebras, 509–29. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0730-2_26.

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Parshin, A. N. "Cancellation Diagrams and Equations Over Groups." In Algebra VII, 90–105. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58013-0_5.

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Gorodentsev, Alexey L. "Calculus of Arrays, Tableaux, and Diagrams." In Algebra II, 75–98. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50853-5_4.

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Carlson, Jon F. "Examples and diagrams." In Modules and Algebras, 42–52. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9189-9_7.

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Cheng, Peter C. H. "Algebra Diagrams: A HANDi Introduction." In Diagrammatic Representation and Inference, 178–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31223-6_20.

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Savage, Alistair. "String Diagrams and Categorification." In Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, 3–36. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63849-8_1.

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Conference papers on the topic "Diagram algebra"

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Weiglein, G. "Feynman-diagram evaluation in the electroweak theory with computer algebra." In ADVANCED COMPUTING AND ANALYSIS TECHNIQUES IN PHYSICS RESEARCH: VII International Workshop; ACAT 2000. AIP, 2001. http://dx.doi.org/10.1063/1.1405260.

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Yingjuan Xu. "The formal semantics of UML activity diagram based on Process Algebra." In 2011 International Conference on Computer Science and Service System (CSSS). IEEE, 2011. http://dx.doi.org/10.1109/csss.2011.5974744.

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Guang-yi Tang, Bo Yu, Ji-ge Li, and Deng-ju Yao. "Study on UML state diagram semantic equivalence based on process algebra." In International Conference on Software Intelligence Technologies and Applications & International Conference on Frontiers of Internet of Things 2014. Institution of Engineering and Technology, 2014. http://dx.doi.org/10.1049/cp.2014.1543.

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Enjo, Hidekazu, Motonari Tanabu, and Junichi Iijima. "A syntactical foundation of class diagram algebra for enterprise service systems." In 2010 7th International Conference on Service Systems and Service Management (ICSSSM 2010). IEEE, 2010. http://dx.doi.org/10.1109/icsssm.2010.5530206.

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Morgado Hernández, Cindy, and Gabriel Yáñez Canal. "Bayesian reasoning: connecting arithmetic, algebra and tree diagrams. A longitudinal research." In Advances in Statistics Education: Developments, Experiences, and Assessments. International Association for Statistical Education, 2015. http://dx.doi.org/10.52041/srap.15111.

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This paper shows some of the results of the research conducted with the purpose of knowing the Bayesian reasoning of college students doing their first course in probability and statistics. For this there three tests that were designed and implemented at different times during the semester. The results showed three stages in the reasoning of the students: the first, which coincides with the first test, is characterized by the use of mathematical arguments proportions; the second, which coincides with the second test is characterized by the joint use of tree diagrams and algebraic expression of Bayes which had been taught by teachers; the third, which coincides with the third test, is characterized by the failed recall Bayes rule and incomplete use of the tree diagram attempt.
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Enjo, Hidekazu, Motonari Tanabu, and Junichi Iijima. "A step toward foundation of class diagram algebra for enterprise service systems." In 2009 6th International Conference on Service Systems and Service Management. IEEE, 2009. http://dx.doi.org/10.1109/icsssm.2009.5174926.

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Margetts, Rebecca, and Roger F. Ngwompo. "Comparison of Modeling Techniques for a Landing Gear." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39722.

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A wide range of modeling techniques is available to the engineer. The objective of this paper is to compare some typical modeling techniques for the simulation of a multi-domain mechatronic system. Usual dynamic modeling methods, such as block diagrams and iconic diagrams, can cause problems for the engineer. Differential algebraic equations (DAEs) and algebraic loops can significantly increase simulation times and cause numeric errors. Bond graphs are less common in industry, and are presented here as a method which allows the engineer to easily identify causal loops and elements in differential causality. These can indicate DAEs in the underlying equations. An aircraft landing gear is given as an example of a multi-domain system, and is modeled as a block diagram, an iconic diagram and as a bond graph. The time to construct the model, time to solve and problems faced by the analyst are presented. Bond graphs offer distinct advantages in terms of the ease of implementing algebraic equations and visibility of causality. The time taken to model a system can be significantly reduced and the results appear free from computational errors. Bond graphs are therefore recommended for this type of multi-domain systems analysis.
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8

Dongxu, Liu, Xu Dongling, Zhang Shuhui, and Hu Xiaoying. "A Quantitative Approach for Reliability Evaluation of Safety I&C Systems in Nuclear Power Plants." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66483.

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The probability that the safety I&C system fails to actuate or advertently actuates RT or ESF functions, in part, essentially determines whether a nuclear power plant could operate safely and efficiently. Since more conservative assumptions and simplifications are introduced during the analysis, this paper achieves solid results by performing the modeling and calculation based on a relatively simple approach, the reliability block diagram (RBD) method. A typical safety I&C platform structure is involved in the model presented in this paper. From the perspective of conservation and simplicity, some assumptions are adopted in this paper. A group of formulas is derived in this paper based on Boolean algebra, probability theory, basic reliability concepts and equations, to facilitate the calculations of probabilities that the safety I&C system fails to actuate or advertently actuates RT or ESF functions. All the inputs of the analysis and calculation in this paper, which includes the I&C platform structure, the constitution of the hardware modules, and reliability data, are referenced to the nuclear power plant universal database where applicable. Although the conclusion drawn in the paper doesn’t apply to the I&C platform assessment for a specific plant, the method of modeling and process of analysis provides an illustration of an alternative quantitative reliability assessment approach for a typical safety I&C system installed in the nuclear power plant.
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Nganyewou Tidjon, Lionel, Marc Frappier, Michael Leuschel, and Amel Mammar. "Extended Algebraic State-Transition Diagrams." In 2018 23rd International Conference on Engineering of Complex Computer Systems (ICECCS). IEEE, 2018. http://dx.doi.org/10.1109/iceccs2018.2018.00023.

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10

Wang, Randi, and Vadim Shapiro. "Topological Semantics for Lumped Parameter Systems Modeling." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98181.

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Abstract Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of ordinary differential and algebraic equations. Languages and simulation tools for modeling such systems differ in syntax, informal semantics, and in the methods by which such systems of equations are generated and simulated, leading to numerous interoperability challenges. We propose to unify semantics of all such systems using standard notions from algebraic topology. In particular, Tonti diagrams classify all physical theories in terms of physical laws (topological and constitutive) defined over a pair of dual cochain complexes and may be used to describe different types of lumped parameter systems. We show that all possible methods for generating the corresponding state equations within each physical domain correspond to paths over Tonti diagrams. We further propose a generalization of Tonti diagram that captures the behavior and supports canonical generation of state equations for multi-domain lumped parameter systems. The unified semantics provides a basis for greater interoperability in systems modeling, supporting automated translation, integration, reuse, and numerical simulation of models created in different authoring systems and applications. Notably, the proposed algebraic topological semantics is also compatible with spatially and temporally distributed models that are at the core of modern CAD and CAE systems.
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